1. Why?
SFML sets these states once during initialization, setting them everytime Draw is called would be redundant.
Use sf::Window if you want to draw with OpenGL instead of SFML.
2. Do I need to do it once or every frame?
Just once but then Draw() is unlikely to work correctly after you do so. But you probably won't call it, so use sf::Window instead.
3. Are there more opengl settings I need to set to make it act as if it's a new context?
Yes. Use a sf::Window instead.
4. Is there a way to avoid having to set them?
Use sf::Window.